# laed5 - Man Page

laed5: D&C step: secular equation, 2x2

## Synopsis

### Functions

subroutine dlaed5 (i, d, z, delta, rho, dlam)
DLAED5 used by DSTEDC. Solves the 2-by-2 secular equation.
subroutine slaed5 (i, d, z, delta, rho, dlam)
SLAED5 used by SSTEDC. Solves the 2-by-2 secular equation.

## Function Documentation

### subroutine dlaed5 (integer i, double precision, dimension( 2 ) d, double precision, dimension( 2 ) z, double precision, dimension( 2 ) delta, double precision rho, double precision dlam)

DLAED5 used by DSTEDC. Solves the 2-by-2 secular equation.

Purpose:

``` This subroutine computes the I-th eigenvalue of a symmetric rank-one
modification of a 2-by-2 diagonal matrix

diag( D )  +  RHO * Z * transpose(Z) .

The diagonal elements in the array D are assumed to satisfy

D(i) < D(j)  for  i < j .

We also assume RHO > 0 and that the Euclidean norm of the vector
Z is one.```
Parameters

I

```          I is INTEGER
The index of the eigenvalue to be computed.  I = 1 or I = 2.```

D

```          D is DOUBLE PRECISION array, dimension (2)
The original eigenvalues.  We assume D(1) < D(2).```

Z

```          Z is DOUBLE PRECISION array, dimension (2)
The components of the updating vector.```

DELTA

```          DELTA is DOUBLE PRECISION array, dimension (2)
The vector DELTA contains the information necessary
to construct the eigenvectors.```

RHO

```          RHO is DOUBLE PRECISION
The scalar in the symmetric updating formula.```

DLAM

```          DLAM is DOUBLE PRECISION
The computed lambda_I, the I-th updated eigenvalue.```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Contributors:

Ren-Cang Li, Computer Science Division, University of California at Berkeley, USA

Definition at line 107 of file dlaed5.f.

### subroutine slaed5 (integer i, real, dimension( 2 ) d, real, dimension( 2 ) z, real, dimension( 2 ) delta, real rho, real dlam)

SLAED5 used by SSTEDC. Solves the 2-by-2 secular equation.

Purpose:

``` This subroutine computes the I-th eigenvalue of a symmetric rank-one
modification of a 2-by-2 diagonal matrix

diag( D )  +  RHO * Z * transpose(Z) .

The diagonal elements in the array D are assumed to satisfy

D(i) < D(j)  for  i < j .

We also assume RHO > 0 and that the Euclidean norm of the vector
Z is one.```
Parameters

I

```          I is INTEGER
The index of the eigenvalue to be computed.  I = 1 or I = 2.```

D

```          D is REAL array, dimension (2)
The original eigenvalues.  We assume D(1) < D(2).```

Z

```          Z is REAL array, dimension (2)
The components of the updating vector.```

DELTA

```          DELTA is REAL array, dimension (2)
The vector DELTA contains the information necessary
to construct the eigenvectors.```

RHO

```          RHO is REAL
The scalar in the symmetric updating formula.```

DLAM

```          DLAM is REAL
The computed lambda_I, the I-th updated eigenvalue.```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Contributors:

Ren-Cang Li, Computer Science Division, University of California at Berkeley, USA

Definition at line 107 of file slaed5.f.

## Author

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## Info

Tue Nov 28 2023 12:08:43 Version 3.12.0 LAPACK